Session J30: Circuit Theory, Hamiltonian Analysis and Design Tools I

Live

Superconducting quantum circuits is one of the leading candidates for a universal quantum computer. Designing these circuits requires the ability simulate and analyze the properties of a general superconducting circuit. In particular, going outside the transmon approach, we cannot make assumptions on anharmonicity, thus precluding blackbox quantization approaches. We consider a few issues involved in simulating general superconducting circuits. One of the issues often faced is the handling of free modes in the circuit, that is, circuit modes with vanishing frequency. Another issue is circuit size, namely the challenge of simulating large circuits. The main mathematical tool we use to address these issues is linear canonical transformations in the setting of quantum mechanics. We address the first issue by giving a provably correct algorithm for removing free modes by performing a linear canonical transformation to completely decouple the free modes from other circuit modes. We address the second by giving a series of different linear canonical transformations to reduce inter-mode couplings, thereby reducing the overhead for classical simulation.   

Live

Superconducting circuits have evolved into major contenders as quantum bits in the race towards quantum computation. The quantitative modeling of the spectral and coherence properties of such circuits is a cornerstone underlying all research employing superconducting qubits in quantum information science. Fundamentally based on circuit quantization, the path from a simple circuit network to predicting a qubit's energy levels and coherence times faces a number of common challenges. Several open-source packages exist that streamline the modeling of superconducting qubits using different strategies. After a review of the scope of available packages, this talk will focus on an introduction to scQubits, a Python package for superconducting qubits. I will illustrate capabilities of scQubits in predicting spectra and coherence properties, and give examples for exploring different qubit parameter regimes. Going beyond the level of a single qubit, scQubits offers simple ways to build up composite systems of multiple qubits and harmonic modes, and provides a convenient interface to QuTiP, making it easy to simulate advanced closed and open-system dynamics of circuit QED systems.   

Live

The performance of a superconducting quantum device or processor rests heavily on our ability to predictively model its quantum effects at unprecedented levels of precision and optimization. Here, we revisit and generalize the hybrid classical-quantum approach to the design of circuit quantum electrodynamic structures incorporating qubits and distributed transmission-line resonators. We formulate the problem in a topological manner and use the energy-participation ratio (EPR) of the distributed resonator eigenmodes as a shortcut in quantizing the effective white-box model. We present improvements in agreement over the naive theory when compared to experimental results across 10 devices, which incorporate transmon qubits coupled to varying numbers of resonant structures.   

Live

When performing large-scale quantum computation, a superconducting qubit is often read out by its dispersive coupling with an auxiliary cavity. The readout mechanism is based on Rabi model with large detuning. However, because of virtual excitation exchange, this approach is are usually significantly limited by the Purcell effects. By considering a superconducting qubit nonperturbative dispersive coupling (NPDC) to a frequency-tunable measurement resonator,we show [1] how to realize an ideal QND readout of a superconducting qubit.The NPDC-based readout mechanism is free of dipole-field interactions, and is not deteriorated by intracavity photons. Moreover, the NPDC can be conveniently turned on/off via an external control flux. Our proposal can be extended to a multiqubit architecture for a joint qubit readout. The work of R. Dassonneville et al. [2] describes a protocol very similar to ours, and can be viewed as an experimental realization of the QND measurement of qubits via the NPDC mechanism proposed by us much earlier in [1].
[1] X. Wang, A. Miranowicz, and F. Nori, Phys. Rev. Applied 12, 064037 (2019)
[2] R. Dassonneville et al., Phys. Rev. X 10, 011045 (2020)   

Live

We propose a formalism that allows to determine whether an arbitrary superconducting circuit can act as a protected qubit. We do that by analyzing the phase-space topology of the studied circuit. The Hamiltonian of a superconducting circuit is a function of charge and phase variables. Instead of treating the space of n phase variables describing the circuit as a real vector space Rⁿ, we treat the phase space as a more complex manifold whose topology is determined by charge quantization in the superconducting circuit. This small change in approaching the Schrodinger equation has far-reaching consequences in terms of understanding topologically protected subspaces. Our approach provides a generalization for the stabilizer formalism. Most importantly, we show how it can be used to systematically search for new protected qubit designs.   

Live

A standard approach for describing weakly anharmonic superconducting qubits coupled to cavities is “black-box quantization” [1], where the nonlinearity is written using the eigenmodes of the linear problem. This approach (as typically used) misses dissipative effects that are higher-order in the nonlinearity. In this work, we develop analytic methods based on the Keldysh technique and Lindblad perturbation theory that systematically describe such higher-order dissipative effects. These approaches offer advantages over traditional Schrieffer-Wolff methods and provide simple analytic descriptions of qubit dephasing and relaxation. Our work provides new theoretical tools that could be useful in a variety of different settings. They could also help shed light on the somewhat surprising photon number dependence of qubit relaxation seen in many experiments.

[1] S. Nigg, et al., Phys. Rev. Lett. 108, 240502 (2012).   

Live

Flux qubit design is a task of choosing the best fabrication and control parameters for some desired protocol of quantum annealing. Conventionally it is done through experiments, circuit simulation and non-rigorous noise estimates. Our long-term goal is to develop a simplified rigorous theoretical model where the task of qubit design can be defined and leads to a non-trivial optimum for the fabrication and control parameters. To that end, we study circuit models for a variety of flux qubits in the large barrier regime, where the problem is analytically tractable. This still allows one to do a full anneal starting with a superposition of the ground states of each well, and in fact modern capacitively shunted flux qubit (CSFQ) experiments choose the schedule in this way. We compute an adiabatic timescale of the qubit approximation, characterizing the leakage to the non-qubit states. We find that this leakage leads to a “freezeout” of the coherent tunneling close to the end of the anneal even in the closed system setting.   

Live

As quantum circuits grow in complexity, it is crucial to have precise but practical methods for characterization, optimization and scaling of the two-qubit gates. Here, we present a theoretical study of cross-resonance (CR) covering gate parameters, gate error, spectator qubits and multi-qubit frequency collisions [1]. Our analysis is based on obtaining an effective gate Hamiltonian using Schrieffer-Wolff perturbation theory [2]. Accounting for Josephson nonlinearity, we derive an improved starting model with renormalized qubit-qubit and drive interaction rates leading to an approximately 15 percent relative correction of the effective gate parameters compared to Kerr theory. The gate operation strongly depends on the ratio of qubit-qubit detuning and anharmonicity. We characterize five distinct regions of operation and propose optimal parameters to achieve high gate speed and low coherent gate error. Our characterization of spectator qubits and collisions lays out the groundwork for scaling up CR gates in a quantum processor.
[1]. Phys. Rev. A 102, 042605
[2]. Phys. Rev. A 101, 052308   

Live

Development of quantum architectures during the last decade has inspired hybrid classicalquantum algorithms in physics and quantum chemistry that promise simulations of fermionic systems beyond the capability of modern classical computers, even before the era of quantum computing fully arrives. Strong research efforts have been recently made to obtain minimal depth quantum circuits which could accurately represent chemical systems. Here, we show that unprecedented methods used in quantum chemistry, designed to simulate molecules on quantum processors, can be extended to calculate properties of periodic solids. In particular, we present minimal depth circuits implementing the variational quantum eigensolver algorithm and successfully use it to compute the band structure of silicon on a quantum machine for the first time. We are convinced that the presented quantum experiments performed on cloud-based platforms will stimulate more intense studies towards scalable electronic structure computation of advanced quantum materials   

Live

In superconducting circuits interrupted by Josephson junctions, the energy spectrum is determined by the symmetries of the Josephson potential and depends on offset charges on different islands modulo 2e via the Aharonov-Casher effect, resembling a crystal band structure. We show that by exploiting 4e tunnel junctions effectively described by a cos(2φ) energy-phase relation, where tunneling of pairs of Cooper pairs dominates, or by introducing semiconducting wires hosting Majorana end fermions realizing single e tunnel junction via the 4π Josephson effect, we can engineer the Josephson potential and design spectra featuring flat bands and multiple pairs of Dirac points, that can be used to park the qubits in charge noise free states or manipulate Majorana qubits.   

Live

The design of experimental devices for superconducting quantum circuits is a difficult and time-consuming process. Here, we present an open-source framework to simplify and streamline the design, simulation, and analysis of quantum devices. We illustrate the improved workflow through an example of a multi-qubit design from start to finish. In particular, we highlight auto-routing algorithms and the built-in quantization analysis, such as the lumped-oscillator model and the energy participation ratio (EPR) method. We conclude with our near-term vision for turning this project, nicknamed “Qiskit Metal,” into a widely-helpful toolkit for the community.   

On Demand

Quantum defects within materials, identified as Two-Level Systems (TLSs), cause noise in astronomy kinetic inductance detectors (KIDs) and quantum information processors. Recognizing that TLSs will generally cause phase noise in KIDs, we develop a device which can potentially allow one to distinguish the intended photon signal from TLS noise. Here we report on a theory and experimental study of such a device. The device consists of two superconducting resonators sharing an electrical capacitance bridge that allows possible distinction between signal and noise. In the fabricated device, TLSs are within a deposited amorphous film that is the dielectric of the capacitors. One resonator mode uses TiN as an inductor and allows tuning of one bare resonator frequency into degeneracy with the other. Once tuned in this way, the resonator modes hybridize and the resonator field is zero in 2 of the 4 capacitors for each of the two hybridized modes. We find that with this so-called zero detuning, the individual resonator modes shift in an uncorrelated way from single-TLS noise, since each hybridized mode samples different TLSs . In contrast, the intended signal to one inductor of the KID induces known correlated changes to both modes such that they can be distinguished from TLS noise.